Combined time-integrated CP asymmetry A_CP and B(K_S to mu mu) measurements, using known B(K_L to mu mu) and B(K_L to gamma gamma), extract the short-distance amplitude |A^2 lambda^5 eta-bar| and resolve the discrete ambiguity in the SM prediction for B(K_L to mu mu).
$K \rightarrow \pi\pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
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abstract
We present new results for the amplitude $A_2$ for a kaon to decay into two pions with isospin $I=2$: Re$A_2 = 1.50(4)_\mathrm{stat}(14)_\mathrm{syst}\times 10^{-8}$ GeV; Im$A_2 = -6.99(20)_\mathrm{stat}(84)_\mathrm{syst}\times 10^{-13}$ GeV. These results were obtained from two ensembles generated at physical quark masses (in the isospin limit) with inverse lattice spacings $a^{-1}=1.728(4)$ GeV and $2.358(7)$ GeV. We are therefore able to perform a continuum extrapolation and hence largely to remove the dominant systematic uncertainty from our earlier results, that due to lattice artefacts. The only previous lattice computation of $K\to\pi\pi$ decays at physical kinematics was performed using an ensemble at a single, rather coarse, value of the lattice spacing ($a^{-1}\simeq 1.37(1)$ GeV). We confirm the observation that there is a significant cancellation between the two dominant contributions to Re$A_2$ which we suggest is an important ingredient in understanding the $\Delta I=1/2$ rule, Re$A_0$/Re$A_2\simeq 22.5$, where the subscript denotes the total isospin of the two-pion final state. Our result for $A_2$ implies that the electroweak penguin contribution to $\epsilon^\prime/\epsilon$ is Re($\epsilon^\prime/\epsilon)_\textrm{EWP}=-(6.6\pm 1.0)\times 10^{-4}$.
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The paper proposes capturing all ΔI=1/2-enhanced isospin-breaking effects on ε' via QCD+QED lattice simulations limited to photons with energies 0.5-2.0 GeV, with a ChPT estimate placing the low-energy contribution at ~0.5%.
The FLAG 2024 review provides updated averages of lattice QCD determinations for quark masses, decay constants, form factors, mixing parameters, and nucleon matrix elements.
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CP violation in $K\to\mu^+\mu^-$ with and without time dependence through a tagged analysis
Combined time-integrated CP asymmetry A_CP and B(K_S to mu mu) measurements, using known B(K_L to mu mu) and B(K_L to gamma gamma), extract the short-distance amplitude |A^2 lambda^5 eta-bar| and resolve the discrete ambiguity in the SM prediction for B(K_L to mu mu).
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Isospin breaking corrections to a lattice QCD calculation of $\varepsilon'$
The paper proposes capturing all ΔI=1/2-enhanced isospin-breaking effects on ε' via QCD+QED lattice simulations limited to photons with energies 0.5-2.0 GeV, with a ChPT estimate placing the low-energy contribution at ~0.5%.
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FLAG Review 2024
The FLAG 2024 review provides updated averages of lattice QCD determinations for quark masses, decay constants, form factors, mixing parameters, and nucleon matrix elements.